Optimal. Leaf size=66 \[ \frac {2033647}{512 (1-2 x)^2}-\frac {6206585}{256 (1-2 x)}-\frac {3907293 x}{128}-\frac {747297 x^2}{64}-\frac {69273 x^3}{16}-\frac {73305 x^4}{64}-\frac {1215 x^5}{8}-\frac {8117095}{256} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} -\frac {1215 x^5}{8}-\frac {73305 x^4}{64}-\frac {69273 x^3}{16}-\frac {747297 x^2}{64}-\frac {3907293 x}{128}-\frac {6206585}{256 (1-2 x)}+\frac {2033647}{512 (1-2 x)^2}-\frac {8117095}{256} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {3907293}{128}-\frac {747297 x}{32}-\frac {207819 x^2}{16}-\frac {73305 x^3}{16}-\frac {6075 x^4}{8}-\frac {2033647}{128 (-1+2 x)^3}-\frac {6206585}{128 (-1+2 x)^2}-\frac {8117095}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {2033647}{512 (1-2 x)^2}-\frac {6206585}{256 (1-2 x)}-\frac {3907293 x}{128}-\frac {747297 x^2}{64}-\frac {69273 x^3}{16}-\frac {73305 x^4}{64}-\frac {1215 x^5}{8}-\frac {8117095}{256} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 61, normalized size = 0.92 \begin {gather*} -\frac {1508337+58608500 x-190079460 x^2+81639840 x^3+31266000 x^4+13197888 x^5+4069440 x^6+622080 x^7+32468380 (1-2 x)^2 \log (1-2 x)}{1024 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 51, normalized size = 0.77
method | result | size |
risch | \(-\frac {1215 x^{5}}{8}-\frac {73305 x^{4}}{64}-\frac {69273 x^{3}}{16}-\frac {747297 x^{2}}{64}-\frac {3907293 x}{128}+\frac {\frac {6206585 x}{128}-\frac {10379523}{512}}{\left (-1+2 x \right )^{2}}-\frac {8117095 \ln \left (-1+2 x \right )}{256}\) | \(47\) |
default | \(-\frac {1215 x^{5}}{8}-\frac {73305 x^{4}}{64}-\frac {69273 x^{3}}{16}-\frac {747297 x^{2}}{64}-\frac {3907293 x}{128}+\frac {6206585}{256 \left (-1+2 x \right )}+\frac {2033647}{512 \left (-1+2 x \right )^{2}}-\frac {8117095 \ln \left (-1+2 x \right )}{256}\) | \(51\) |
norman | \(\frac {-\frac {8080231}{128} x +\frac {24514101}{128} x^{2}-\frac {2551245}{32} x^{3}-\frac {1954125}{64} x^{4}-\frac {206217}{16} x^{5}-\frac {63585}{16} x^{6}-\frac {1215}{2} x^{7}}{\left (-1+2 x \right )^{2}}-\frac {8117095 \ln \left (-1+2 x \right )}{256}\) | \(52\) |
meijerg | \(\frac {144 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {1560 x^{2}}{\left (1-2 x \right )^{2}}-\frac {1810 x \left (-18 x +6\right )}{3 \left (1-2 x \right )^{2}}-\frac {8117095 \ln \left (1-2 x \right )}{256}-\frac {4665 x \left (16 x^{2}-36 x +12\right )}{4 \left (1-2 x \right )^{2}}-\frac {5769 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{16 \left (1-2 x \right )^{2}}-\frac {17829 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{64 \left (1-2 x \right )^{2}}-\frac {6885 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{448 \left (1-2 x \right )^{2}}-\frac {1215 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{1024 \left (1-2 x \right )^{2}}\) | \(202\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 51, normalized size = 0.77 \begin {gather*} -\frac {1215}{8} \, x^{5} - \frac {73305}{64} \, x^{4} - \frac {69273}{16} \, x^{3} - \frac {747297}{64} \, x^{2} - \frac {3907293}{128} \, x + \frac {26411 \, {\left (940 \, x - 393\right )}}{512 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {8117095}{256} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 67, normalized size = 1.02 \begin {gather*} -\frac {311040 \, x^{7} + 2034720 \, x^{6} + 6598944 \, x^{5} + 15633000 \, x^{4} + 40819920 \, x^{3} - 56538312 \, x^{2} + 16234190 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 9197168 \, x + 10379523}{512 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 58, normalized size = 0.88 \begin {gather*} - \frac {1215 x^{5}}{8} - \frac {73305 x^{4}}{64} - \frac {69273 x^{3}}{16} - \frac {747297 x^{2}}{64} - \frac {3907293 x}{128} - \frac {10379523 - 24826340 x}{2048 x^{2} - 2048 x + 512} - \frac {8117095 \log {\left (2 x - 1 \right )}}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 47, normalized size = 0.71 \begin {gather*} -\frac {1215}{8} \, x^{5} - \frac {73305}{64} \, x^{4} - \frac {69273}{16} \, x^{3} - \frac {747297}{64} \, x^{2} - \frac {3907293}{128} \, x + \frac {26411 \, {\left (940 \, x - 393\right )}}{512 \, {\left (2 \, x - 1\right )}^{2}} - \frac {8117095}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 46, normalized size = 0.70 \begin {gather*} \frac {\frac {6206585\,x}{512}-\frac {10379523}{2048}}{x^2-x+\frac {1}{4}}-\frac {8117095\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {3907293\,x}{128}-\frac {747297\,x^2}{64}-\frac {69273\,x^3}{16}-\frac {73305\,x^4}{64}-\frac {1215\,x^5}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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